write a go solution for Description:
There is a square matrix, consisting of n rows and n columns of cells, both numbered from 1 to n. The cells are colored white or black. Cells from 1 to a_i are black, and cells from a_i+1 to n are white, in the i-th column.

You want to place m integers in the matrix, from 1 to m. There are two rules:

- each cell should contain at most one integer;
- black cells should not contain integers.

The beauty of the matrix is the number of such j that j+1 is written in the same row, in the next column as j (in the neighbouring cell to the right).

What's the maximum possible beauty of the matrix?

Input Format:
The first line contains a single integer t (1<=t<=10^4) — the number of testcases.

The first line of each testcase contains a single integer n (1<=n<=2*10^5) — the size of the matrix.

The second line contains n integers a_1,a_2,...,a_n (0<=a_i<=n) — the number of black cells in each column.

The third line contains a single integer m (0<=m<=sumlimits_i=1^nn-a_i) — the number of integers you have to write in the matrix. Note that this number might not fit into a 32-bit integer data type.

The sum of n over all testcases doesn't exceed 2*10^5.

Output Format:
For each testcase, print a single integer — the maximum beauty of the matrix after you write all m integers in it. Note that there are no more integers than the white cells, so the answer always exists.

Note:
None. Output only the code with no comments, explanation, or additional text.